Complex variable formulations for usual and hypersingular integral equations for potential problems ? with applications to corners and cracks

Kolhe, R.; Ye, Wenjing; Hui, Chung‐Yuen; Mukherjee, Subrata

doi:10.1007/bf00368550

Cited by 21 publications

(1 citation statement)

References 8 publications

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“…2,6 In particular, a comparison is made here with the results obtained using a novel Galerkin BIE approach to recover du/ds introduced by Gray et al 2 Notice that symmetrical Galerkin BEM (SGBEM) was applied in Reference 2 in the BEM analysis stage to obtain u h and (du/dn) h used as the input data for the recovering procedure. A simple harmonic function u x 2 À y 2 is considered, allowing an easy comparison of the procedure presented with procedures developed by other authors.…”

Section: Numerical Examplesmentioning

confidence: 99%

Potential gradient recovery using a local smoothing procedure in the Cauchy integral

Mantič

Graciani

Parı́s

1999

Commun. Numer. Meth. Engng.

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A new approach for evaluation of the potential gradient in the 2D boundary element method is presented. The two key elements of the procedure developed are, ®rstly, a new Strongly Singular Boundary Integral Representation of Potential Gradient in complex variable formulation (equivalent to the Cauchy integral representation of analytic functions), and secondly a continuous approximation of the integral density of this representation determined by a local smoothing procedure applied to the data obtained from BEM analysis. Numerical tests show the high accuracy of the recovered value of the tangential derivative of the potential on smooth and non-smooth boundaries.

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Section: Numerical Examplesmentioning

confidence: 99%

Potential gradient recovery using a local smoothing procedure in the Cauchy integral

Mantič

Graciani

Parı́s

1999

Commun. Numer. Meth. Engng.

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A complex-variable boundary element approach to fully developed flow and heat transfer in ducts of general cross-section

Fisher

Torrance

1999

Int. J. Numer. Meth. Engng.

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The complex‐variable boundary element method (CVBEM) is used to analyse forced convection in cooling passages with general, convex cross‐sections. Quadratic spline interpolation is employed for the modelling of coupled velocity and temperature fields. The method is well‐suited for ducts with curved surfaces and high geometric aspect ratios. The method is illustrated for ducts with rounded rectangular, elliptical and rounded diamond cross‐sections. General correlations are presented for the fully developed Nusselt number and Moody friction factor, and the Hagenbach entrance region factor. Copyright © 1999 John Wiley & Sons, Ltd.

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Potential gradient recovery using a local smoothing procedure in the Cauchy integral

Mantič

Graciani

Parı́s

1999

Commun. Numer. Meth. Engng.

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SUMMARYA new approach for evaluation of the potential gradient in the 2D boundary element method is presented. The two key elements of the procedure developed are, ®rstly, a new Strongly Singular Boundary Integral Representation of Potential Gradient in complex variable formulation (equivalent to the Cauchy integral representation of analytic functions), and secondly a continuous approximation of the integral density of this representation determined by a local smoothing procedure applied to the data obtained from BEM analysis. Numerical tests show the high accuracy of the recovered value of the tangential derivative of the potential on smooth and non-smooth boundaries.

show abstract

Complex variable formulations for usual and hypersingular integral equations for potential problems ? with applications to corners and cracks

Cited by 21 publications

References 8 publications

Potential gradient recovery using a local smoothing procedure in the Cauchy integral

Potential gradient recovery using a local smoothing procedure in the Cauchy integral

A complex-variable boundary element approach to fully developed flow and heat transfer in ducts of general cross-section

Potential gradient recovery using a local smoothing procedure in the Cauchy integral

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